Scientific Notation

When scientists deal with very large numbers, it’s hard to keep track of place values! How far? 92000000 miles

It is hard with very small numbers, too! How wide is an atom? 0.0000000001 meters wide!

Scientific notation consists of two parts: A number between 1 and 10 A power of 10 N x 10x

We use Short hand ! one googol !!! 10 100 = 10 x 10 1,000 = 10 x 10 x 10 10,000 = 10 x 10 x 10 x 10 100,000 = 10 x 10 x 10 x 10 x 10 1,000,000 = 10 x 10 x 10 x 10 x 10 x 10 10 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 one googol !!!

Standard Form Scientific Notation 200 = 2 x 100 4,000 = 4 x 1000 70,000 = 7 x 10,000 500,000 = 5 x 100,000 3,000,000 = 3 x 1,000,000 Scientific Notation

A short cut 8 000 000 . . Move the point to get a number between 1 and 10 The point moved 6 places 8 000 000 . . Add the decimal point Between 1 and 10

A short cut 92 000 000 . . Move the point to get a number between 1 and 10 The point moved 7 places 92 000 000 . . Add the decimal point Between 1 and 10

Try for yourself: Turn Standard Form into Scientific Notation (1) 30 000 (2) 700 000 (3) 5 300 (4) 470 000 (5) 9 500 000

Add 5 zeros, although you probably won’t need them all. Changing back The point moves 5 places 3.46 00000 . =346,000 Hint: Add 5 zeros, although you probably won’t need them all. Zeros after the point aren’t needed.

Add 7 zeros, although you probably won’t need them all. Changing back The point needs to move 7 places 8.6 0000000 . =86,000,000 Zeros after the point aren’t needed. Hint: Add 7 zeros, although you probably won’t need them all.

Try for Yourself: Change Scientific Notation back to Standard form (1) (2) (3) (4) (5) = 600 000 = 8 000 = 650 000 = 120 000 000 = 3 710 000

Standard Form to Scientific Form for SMALL numbers Move the point to get a number between 1 and 10 0.000 000 000 1 . The point moved 10 places. Negative sign for small numbers.

Standard Form to Scientific Notation for small numbers Move the point to get a number between 1 and 10 0.000 000 76 . The point moved 7 places. Negative sign for small numbers.

Standard Form to Scientific Notation for small numbers Move the point to get a number between 1 and 10 0.000 001 93 . The point moved 6 places. Negative sign for small numbers.

Change Standard Form to Scientific Notation Try for Yourself: Change Standard Form to Scientific Notation (1) 0.000 07 (2) 0.000 45 (3) 0.003 4 (4) 0. 000 724 (5) 0.000 000 494

Changing back small numbers Add 3 zeros to the left of the number. Hint: Add 3 zeros to the left of the number. -3 so remember to move point left 3 spaces. 000 . 2 = 0.002 .

Changing back small numbers Add 5 zeros to the left of the number. -5 so remember to move point left for small numbers. Hint: Add 5 zeros to the left of the number. 00000 . 8.6 = 0.000 086

Changing back small numbers Add 6 zeros to the left of the number. -6 so remember to move point left for small numbers. Hint: Add 6 zeros to the left of the number. 000000 . 5.16 = 0.000 00516

Change Scientific Notation to Standard form Try for Yourself: Change Scientific Notation to Standard form (1) (2) (3) (4) (5) = 0.0005 = 0.00009 = 0.0058 = 0.000 000 62 = 0.000 000 006 032